Question

Delta Cephei is one of the most visible stars in the night sky. Its brightness has periods of 5.4 days, the average brightness is 4.0 and its brightness varies by ±0.35. Find a formula that models the brightness, b, of Delta Cephei as a function of time, t, with t=0 at peak brightness.

Answer 1

Answer:

$y=0.35cos(\frac{2\pi }{5.4 days}x)+4.0$

Explanation:

Since we have peak brightness at t=0 we should use a cosine formula to model this oscillatory phenomena, which will be $y=Acos(kx)+B$. The average of this formula is B, since the cosine part cancels out when averaging, so B=4.0. The brightness variation is the amplitude of the formula, A=0.35, and since $k=\frac{2\pi }{T}$ we finally have $y=0.35cos(\frac{2\pi }{5.4 days}x)+4.0$